I suggest using the simle setup to get a Gmail account going. It will, by default, set up a new Gmail account as IMAP.

Settings > Accounts > Add Account. Enter your email address when prompted, then enter your Gmail password on the Google login screen and accept the permissions requested. You'll then have the option to also sync Contacts and Calendar.

This is also the point where you need to make decisions about how much of your email you want on your device. Tap "Advanced" at the bottom of this screen. Scroll to the very bottom, and set the "Initial Retrieval amount" to "Forever" (or your preferred sync period). You can also set your sync interval here as well. Note that if you'll be syncing a lot of messages, you should be on WiFi, unless you have a very generous data plan.